By construction, the mixed explicit implicit scheme preserves conservation. Further, it was shown in Ref. [1]} that for the linear advection equation \(u_t + c u_x = 0\)  (\(c\)  constant) on a model mesh as given in figure REF , the scheme is monotonicity preserving and total variation diminishing for a time step length \(\Delta t \le \frac{h}{\vert c \vert }\) , i.e., independent of \(\alpha \) . In other words, this way of coupling preserves desirable stability properties. In terms of accuracy, numerical tests for linear advection show first order accuracy for the mixed explicit implicit scheme as described here.
